How to solve polynomials?

polynomials galois-theory

Solution 1:

Solving polynomials of higher degree that are solvable by radicals is a hard problem and there are no general formula. There are many approaches, but most rely on the concept of a Galois resolvent which is an auxiliary polynomial that factors if the original polynomial is solvable. The following papers might be useful:

Solving Solvable Quintics D. S. Dummit Mathematics of Computation Vol. 57, No. 195 (Jul., 1991), pp. 387-401

General Formulas for Solving Solvable Sextic Equations*1 Thomas R. Hagedorn Journal of Algebra Volume 233, Issue 2, 15 November 2000, Pages 704-757

On solvable septics LAU JING FENG http://scholarbank.nus.edu.sg/handle/10635/14460

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